Process, system and software arrangement for a chromatic dispersion compensation using reflective layers in optical coherence tomography (OCT) imaging

ABSTRACT

A system, process and software arrangement are provided to compensate for a dispersion in at least one portion of an image. In particular, information associated with the portion of the image is obtained. The portion of the image can be associated with an interference signal that includes a first electromagnetic radiation received from a sample and a second electromagnetic radiation received from a reference. The dispersion in the at least one portion of the image can be compensated by controlling a phase of at least one spectral component of the interference signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Patent Application Ser. No. 60/575,773 filed on May 29, 2004, the entire disclosure of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to chromatic dispersion compensation in optical coherence tomography (“OCT”) imaging, and more particularly to processes, systems and software arrangements which can compensate for dispersions in OCT images.

BACKGROUND OF THE INVENTION

The spectral-domain variant of optical coherence tomography (“OCT”), called spectral-domain optical coherence tomography (SD-OCT), is a technique is a technology that is suitable for ultrahigh-resolution ophthalmic imaging. This technique has been described in Cense, B. et al., “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography”, Optics Express, 2004 and in International Patent Publication No. WO 03/062802. In addition, U.S. patent application Ser. No. 10/272,171 filed on Oct. 16, 2002 also relates to this subject matter. The axial resolution of an OCT system may be defined in terms of the coherence length (L_(coh)), which can be determined by the center wavelength and bandwidth of the source and the index of refraction of the medium, as described in greater detail in Swanson, E. A. et al., “High-Speed Optical Coherence Domain Reflectometry”, Optics Letters, 1992, 17(2), pp. 151-153. The axial resolution of the OCT system can be improved by using an ultra broadband source, as provided in further detail in Drexler, W. et al., “Enhanced Visualization of Macular Pathology with the Use of Ultrahigh-Resolution Optical Coherence Tomography”, Archives of Ophthalmology, 2003, 121(5), pp. 695-706.

One potential difficulty that may arises from using ultra-broadband sources in a fiber-based OCT setup in, e.g., ophthalmic imaging is the presence of a chromatic dispersion in optically-dense materials like glass, tissue and water. Chromatic dispersion can lead to smearing of the coherence function and/or point spread function in the axial direction, which can significantly affect the image quality. Considerable amounts of dispersion can be tolerated if the dispersion in the two arms of the interferometer is balanced, thus creating a coherence function that would likely to be free from dispersion artifacts. However, when sample and reference arms contain different lengths of optical fiber or other dispersive media, a dispersion mismatch can occur. For example, in the sample arm of an OCT system, the analysis of an eye as a sample with unknown axial length may introduce an unknown amount of chromatic dispersion. Thus, the coherence function may be broadened by an unbalanced dispersion, and the peak intensity of the coherence function can decrease as well. A second order or a group-velocity dispersion can be compensated for using hardware by, e.g., changing the lens to grating distance in a rapid scanning optical delay line. The above has been described in detail in Tearney, G. J. et al., “High-Speed Phase- and Group-Delay Scanning with a Grating-Based Phase Control Delay Line”, Optics Letters, 1997, 22(23), pp. 1811-1813. However, this technique generally does not compensate for higher orders of dispersion. Alternatively, it is possible to balance a dispersion in the OCT system by inserting variable-thickness optical materials with different dispersion properties (such as BK7 and fused silica prisms) in the path of the reference arm or the sample arm. The number of materials with different optical properties that are inserted in the path of the reference arm or the sample arm may determine the number of orders of dispersion one can compensate. The axial length of an eye can vary from one person to another, thus changing the amount of dispersion between patients. Therefore a flexible technique for a dispersion compensation is desirable.

It is possible that, instead of using hardware for such compensation, to use software, and thereby a more flexible compensation easy to adapt to different eyes. Another publication describes a technique to provide an induced dispersion in the delay line of a time domain OCT system that equipped with an optical amplifier based source (e.g., AFC technologies, λ₀=1310 nm, Δλ=75 nm) and compensated for dispersion artifacts in structural intensity images obtained of an onion. See de Boer, J. F. et al., “Stable Carrier Generation and Phase-Resolved Digital Data Processing in Optical Coherence Tomography”, Applied Optics, 2001, 40(31), pp. 5787-5790. Another publication describes a dispersion compensation which is induced by a glass sample. See Fercher, A. F. et al., “Dispersion Compensation For Optical Coherence Tomography Depth-Scan Signals By A Numerical Technique”, Optics Communications, 2002, 204(1-6), pp. 67-74. Their broadband spectrum is generated using a high-pressure mercury lamp. Other dispersion compensation techniques are described in Marks, D. L. et al., “Autofocus Algorithm for Dispersion Correction in Optical Coherence Tomography”, Applied Optics, 2003. 42(16), pp. 3038-3046, Marks, D. L. et al., “Digital Algorithm for Dispersion Correction in Optical Coherence Tomography for Homogeneous and Stratified Media”, Applied Optics, 2003, 42(2), pp. 204-217, and U.S. Pat. No. 5,994,690 which describe an algorithm that used an autocorrelation function to correct image data. However, the above-described problems have not been addressed adequately. Accordingly, there is a need to overcome such deficiencies.

SUMMARY OF THE INVENTION

In contrast to the conventional techniques, the exemplary embodiment of a system, process and software arrangement according to the present invention is capable of using a dispersion broadened reflection of a layer or structure in the biological sample (e.g., retina, skin, coronary artery) to derive parameters to compensate for the chromatic dispersion. One of the advantages of the exemplary system, process and software arrangement according to the present invention is the ease of its implementation, the flexibility thereof, and its adaptation to individual patients or sample locations without the need to make hardware changes so as to compensate for the chromatic dispersion.

According to exemplary embodiments of the present invention, a process, system and software arrangement is provided which can compensate for a dispersion using a numerical technique (e.g., without the need to modify hardware), and can be configured to remove artifacts from OCT images.

In general, a dispersion mismatch between the sample arm and the reference arm of an interferometer may introduce a phase shift e^(tθ(k)) in the cross-spectral density I(k) as a function of wave vector k (k=2π/λ). In a spectral-domain OCT or optical frequency domain interferometry (“OFDI”) setup (as described in Wojtkowski et al., “In Vivo Human Retinal Imaging by Fourier Domain Optical Coherence Tomography”, Journal of Biomedical Optics, 2002, 7(3), pp. 457-463, Nassif, N. et al., “In Vivo Human Retinal Imaging by Ultrahigh-Speed Spectral Domain Optical Coherence Tomography”, Optics Letters, 2004, 29(5), pp. 480-482, Yun, S. H. et al., “High-Speed Optical Frequency-Domain Imaging”, Optics Express, 2003, 11(22), pp. 2953-2963, International Publication No. WO 03/062802 and U.S. Patent Application Ser. No. 60/514,769 filed on Oct. 27, 2004, the spectrometer data can be acquired as a function of a wavelength. Such data may be transformed to k-space. The relation between the phase θ(k) and the multiple orders of dispersion can be described by a Taylor series expansion:

$\begin{matrix} \begin{matrix} {{{{{{\theta(k)} = {{\theta\left( k_{0} \right)} + \frac{\partial{\theta(k)}}{\partial k}}}}_{k_{0}}\left( {k_{0} - k} \right)} + {\frac{1}{2} \cdot \frac{\partial^{2}{\theta(k)}}{\partial k^{2}}}}}_{k_{0}} \\ {{{\left( {k_{0} - k} \right)^{2} + \ldots + {\frac{1}{n!} \cdot \frac{\partial^{n}{\theta(k)}}{\partial k^{n}}}}}_{k_{0}}\left( {k_{0} - k} \right)^{n}} \end{matrix} & (1) \end{matrix}$ with λ₀ being the center wavelength, and k₀ being equal to 2π/λ₀. The first two terms generally describe a constant offset and group velocity, respectively, and are likely not related to dispersive broadening. The third term represents a second order or a group-velocity dispersion. A dispersion mismatch in the sample arm and the reference arm can to a large extend be attributed to this term. However, higher order dispersion terms may contribute to the dispersion mismatch as well, for example when an ultra-broadband source is used.

The dispersion can be removed by multiplying the dispersed cross-spectral density function I(k) with a phase term e^(−tθ(k)). In order to determine the phase term e^(−tθ(k)) to remove the chromatic dispersion and the resulting broadening of the coherence function, data may be obtained with the interferometer using an object in the sample arm with a reflection. This object can be a mirror or a biological sample with a distinct reflection. The spectrum, I(k), acquired with the spectral domain OCT system is Fourier transformed to z-space, resulting in a depth profile of the reflectivity of the sample. A single reflective peak is determined in the depth profile, and the remaining points in the depth profile are set to zero. An inverse transform can be performed to obtain cross spectral density for this single reflective peak. The phase term θ(k) can be approximately equal to the arctangent of the imaginary component divided by the real component.

In order to reduce noise on the phase function and avoid distortion in the image by introducing a group velocity and/or offset in the phase, this function can be fit to a polynomial expression yielding a set of N coefficients α₁-α_(N). Individual spectra may be multiplied with a phase e^(−θ(k)) as determined from the polynomial coefficients, where the first two coefficients of the polynomial fit that correspond to a phase offset and a group velocity are omitted. The chromatic dispersion corrected spectra may then be Fourier transformed to z-space into A-lines, thus resulting in A-lines or depth profiles, where the dispersion has been removed substantially.

In one exemplary embodiment of the present invention, a system, method and software arrangement can be provided to compensate for a dispersion in at least one portion of an image. For example, information associated with the portion of the image is obtained. The portion of the image can be associated with an interference signal that includes a first electromagnetic radiation received from a sample and a second electromagnetic radiation received from a reference. The dispersion in the at least one portion of the image can be compensated by controlling a phase of at least one spectral component of the interference signal. The dispersion may be an indication of a difference between the first and second electromagnetic radiations. In addition, the dispersion may be compensated by reducing and/or removing the dispersion in the portion of the image. Further, data associated with reflective layers in a tissue of the sample may be determined from the interference signal, and information associated with the dispersion that is provided in the data can be obtained. Such information may be used to reduce and/or remove the dispersion from the data. The phase of the spectral component of the portion of the image can be controlled using software.

According to another exemplary embodiment of the present invention, prior to controlling the phase of the at least one spectral component of the interference signal, the dispersion may be quantified, and the dispersion may be corrected for in the image based on the quantification. The dispersion can be a chromatic dispersion. Data associated with the dispersion of the image may also be determined, the dispersion quantified using the data, and the dispersion in the image corrected for based on the quantification. The sample may be a retina of an eye, and the information may include data associated with spectral reflections obtained from the retina. Further, an operator may be enable to select at least one dispersed spectral reflection of the spectral reflections. The dispersed spectral reflection may be selected using a graphical user interface, e.g., during an acquisition of the image and/or after the acquisition of the image. The dispersion can be quantified using the dispersed spectral reflection, and corrected for in the image based on the quantification. A brightest one of the spectral reflections may be interactively searched for, the dispersion quantified using the brightest one of the spectral reflections, and corrected for in the image based on the quantification.

According to still another exemplary embodiment of the present invention, the dispersion can be a depth dependent chromatic dispersion. The information may include dispersed image data, and the dispersion may be quantified using the dispersed image data, and corrected for in the image based on the quantification. The sample may be a retina of an eye, and the dispersed image data may includes spectral reflections. The dispersion may be quantified using the spectral reflections.

In a further exemplary embodiment of the present invention, the dispersion can be compensated for by correcting the dispersion in the image using predetermined constant chromatic dispersion parameters, e.g., based on an estimate of an axial eye length and/or an estimate of an axial eye length.

Other features and advantages of the present invention will become apparent upon reading the following detailed description of embodiments of the invention, when taken in conjunction with the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the invention will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the invention, in which:

FIG. 1 is a block diagram of an exemplary embodiment of a spectral domain optical coherence tomography (“SD-OCT”) arrangement according to the present invention which is capable of implementing the exemplary embodiments of the system, process and software arrangement according to the present invention;

FIG. 2 is a block diagram of an exemplary embodiment of an optical frequency domain intereferometry (“OFDI”) arrangement according to the present invention which is capable of implementing the exemplary embodiments of the system, process and software arrangement according to the present invention;

FIG. 3 is an exemplary graph illustrating an absolute value/depth which can be used for the exemplary embodiments of the system, process and software arrangement according to the present invention;

FIG. 4 is an exemplary graph illustrating curves without dispersion compensation, and with the dispersion compensation applied according to the exemplary embodiment of the present invention;

FIG. 5 is an exemplary graph of a phase θ(k) obtained according to an exemplary embodiment of the present invention from a model eye and from a spectral reflection in a fovea;

FIG. 6 is a retinal image of a human subject which include spectral reflections that may be utilized according to an exemplary embodiment of the present invention;

FIG. 7 is an exemplary image that may be obtained from a human subject, which illustrates the fovea after the dispersion compensation according to an exemplary embodiment of the present invention has been applied;

FIG. 8 is an exemplary graph of a coherence function obtained from a reflective spot in the fovea obtained using an exemplary embodiment of the present invention;

FIG. 9 is a high level flow diagram of a process according to an exemplary embodiment of the present invention;

FIG. 10 is another exemplary image that may be obtained from a human subject, in which a portion of dispersion can be selected via software by an operator; and

FIG. 11 is a detailed flow diagram of a process according to yet another exemplary embodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 shows an exemplary embodiment of a sample configuration of a spectral domain optical coherence tomography (“SD-OCT”) arrangement which can be used for implementing the exemplary embodiments of the system, process and software arrangement according to the present invention. A detailed description of operation of this arrangement is described in detail in International Patent Publication No. WO 03/062802. In particular, as shown in FIG. 1, a high-powered superluminescent diode source (“HP-SLD”) 10 generates an electromagnetic radiation or light signal which is transmitted through a first polarization controller (“PC”) 20′ and an optical isolator 30 so as to facititate a one way propegation of an electromagnetic energy to reach a signal splitter 40. The signal splitter forwards one portion of the split signal to a reference arm (which includes a second PC 20″, a reference, certain optics and a neutral density filter (“NFD”) 50) and another portion of the split signal to a sample arm (which includes a third PC 20′″, certain optics and a sample 60 such as the eye). Thereafter, an electromagnetic signal is reflected from the sample 60 and is combined with the light from the reference arm to form an interference signal. This interference signal is forwarded to a fourth PC 20″″, and forwarded to a collimator (“Col”) 70, a transmission grating (“TG”) 80, an air-spaced focusing lens (“ASL”) 90, and a linescan camera (“LSC”) 100 to be detected by a detecting arrangement (e.g., provided in the linescan camera), and then analyzed by a processing arrangement, e.g., a computer (not shown). Such processing arrangement is capable of implementing the various exemplary embodiments of the system, process and software arrangement according to the present invention.

FIG. 2 shows an exemplary embodiment of an optical imaging frequency domain intereferometry (“OFDI”) arrangement according to the present invention which is capable of implementing the exemplary embodiments of the system, process and software arrangement according to the present invention. A detailed description of various embodiments of the OFDI arrangement is provided in U.S. Patent Application Ser. No. 60/514,769. For example, the light source may be a wavelength-swept source 110. In order to generate a synchronization signal, a portion of the laser output (for example −20%) is obtained, and detected using a fast InGaAs photo-detector through a narrowband fixed-wavelength filter. The detector generates a pulse when the output spectrum of the laser sweeps through the narrow passband of the filter. The detector pulse is fed to a digital circuit 120, e.g., a synchronous TTL pulse generator, for converting the resultant signal to a TTL pulse train. The TTL pulses are used to generate gating pulses for signal sampling. 90% of the remaining light is directed to the sample arm and 10% to the reference mirror 130. This exemplary arrangement can utilize an optical probe based on a galvanometer mirror (e.g., scanner) 140 and an imaging lens. The galvanometer-mounted mirror 140 is controlled by a glava-driver 145 so as to scan the probe light transversely on the sample 60. The total optical power illuminated on the sample 60 may be approximately 3.5 mW. The light reflected from the reference mirror 130 and the sample 60 is received through magneto-optic circulators 150′, 150″, and combined by a 50/50 coupler 160. A fiber-optic polarization controller may be used in the reference arm to align polarization states of the reference and sample arms.

In general, a relative intensity noise (“RIN”) of the received light signal may be proportional to a reciprocal of the linewidth, and the relatively high RIN can be reduced by dual balanced detection (e.g., using a dual balanced receiver 170). The differential current of two InGaAs detectors D1 and D2 in the receiver 170 may be amplified using trans-impedance amplifiers (“TIA”) having a total gain of 56 dB, and passed through a low pass filter (“LPF”) with a 3-dB cutoff frequency at approximately half the sampling rate. The common-noise rejection efficiency of the receiver 170 may be typically greater than 20 dB. In addition to the RIN reduction, the balanced detection may provide other significant benefits—a suppression of a self-interference noise originating from multiple reflections within the sample and optical components; an improvement in the dynamic range; and a reduction of a fixed-pattern noise by greatly reducing the strong background signal from the reference light. Thereafter, a detecting arrangement 180 receives such signals, and forward them to a processing arrangement 190 (e.g., a computer) which implements the exemplary embodiments of the system, process and software arrangement according to the present invention to reduce dispersion, and assist in displaying a resultant image that is based on the original image and the reduction of the dispersion.

Both of these exemplary arrangements, e.g., the SD-OCT arrangement described above with reference to FIG. 1 and the OFDI arrangement described above with reference to FIG. 2, are capable of generating a spectrum I(k) as a function of wave vector k. To determine the phase term, the spectrum I(k) can be Fourier transformed to z-space. FIG. 3 shows an exemplary graph 200 providing an illustration of the curve of an absolute value Abs(I(z)) for z>0 of the Fourier transformed spectrum I(k) vs. depth, with I(z)=FFT(I(k)). As shown in FIG. 3, a dispersion broadened peak may be observed at a depth of approximately 0.6 mm. The function I(z) may be shifted such that the coherence function is centered on the origin. A window can be selected around the coherence function so as to possibly eliminate coherence functions from other reflective structures in the depth profile, and all values outside the window may be set equal to zero. A complex spectrum in k-space may be obtained after an inverse Fourier transformation. The phase term θ(k) can be equal to the arctangent of the imaginary component divided by the real component. Such term can indicate by how much are the subsequent wave numbers k out of phase with each other. According to one example, this function can be provided to a polynomial expression of 9^(th) order, yielding a set of coefficients α₁₋₉.

According to one exemplary embodiment of the present invention, individual spectra may be multiplied with a phase e^(−iθ(k)) as determined from the previous seven polynomial coefficients, where the first two polynomial coefficients may be set to zero, and then inversely Fourier transformed into A-lines, thus removing dispersion. The original and resulting exemplary coherence functions are illustrated in FIG. 4. In particular, the curve of FIG. 4 shows the results without the dispersion compensation is shown as a dashed line, and referred to by numeral 210, and the curve illustrating the results after the dispersion compensation has been successfully applied which is shown as a solid line, and referred to by numeral 220.

FIG. 5 shows a an illustration which aids in the determination of the phase function θ(k) based on certain measurements according to an exemplary embodiment of the present invention, as well as the phase function that subtracts the polynomial fit of 9^(th) order to the phase function. The phase θ(k) may be obtained from a mirror in a model eye and from a spectral reflection in the fovea (e.g., the left axis).

In another example according to the present invention, in vivo human data may be used to determine the phase function for an optimal dispersion compensation. FIG. 6 shows an exemplary retinal image of a human subject, in which three spectral reflections 300, 310, 320 are marked with arrows. These exemplary reflections 300, 310, 320 originate from an internal limiting membrane on top of the retinal nerve fiber layer and the foveolar umbo and from the external limiting membrane. Unmarked, still visible is an exemplary spectral reflection on the surface between the inner and outer segments of the photoreceptor layer, just below the external limiting membrane. FIG. 6 shows typical examples of strong reflections in an image that can be used to determine the phase function for the optimal dispersion compensation.

In order to determine this phase term for the dispersion compensation of data obtained in the sample (e.g., the human eye) in vivo, it is preferable to use a coherence function obtained from a well-reflecting reference point in the eye. In this example, the reflection of the foveal umbo can be used. Other regions in the eye may also create spectral reflections. Spectral reflections may be present from the interface between the inner and outer segments of the photoreceptor layer (“IPRL”) and retinal pigmented epitheleum (“RPE”). In addition, spectral reflections may also be found on the inner limiting membrane, e.g., on top of the retinal nerve fiber layer. For example, five depth profiles may be selected that can illustrate a strong reflection from the foveal umbo. A window can be selected such that it is centered at these strong reflections, and the remaining points may be set to zero. The phase function θ(k) may then be determined as described herein above. In particular, the phase function θ(k) as shown in FIG. 5, can be determined from this measurement, as well as based on the phase function minus the polynomial fit of 9^(th) order to the phase function.

Individual spectra of the image can be first multiplied with a phase e^(−iθ(k)) as determined from the last seven polynomial coefficients, and then inversely Fourier transformed into A-lines, thus removing dispersion. The fit to the dispersion data as determined from the well reflecting reference point in the eye can be a polynomial of any order. Use of a 9^(th) order polynomial was demonstrated. Instead of a polynomial, the data can be fitted to a Fourier series or any other known function set so as to determine a set of coefficients. One of the advantages of using e.g., a polynomial of limited order to filter the dispersion curve is a better immunity to noise of the determined phase correction function.

FIG. 7 shows an exemplary image that may be obtained from a human subject, which illustrates the fovea after the dispersion compensation. The spectral reflection marked with an R can be first used to determine the amount of a chromatic dispersion (as described above), and to remove the chromatic dispersion. The dimensions of the image illustrated in FIG. 7 are 3.1 mm×0.61 mm. Layers in this image are labeled as follows: RNFL—retinal nerve fiber layer; GCL—ganglion cell layer; IPL—inner plexiform layer; INL—inner nuclear layer; OPL—outer plexiform layer; ONL—outer nuclear layer; ELM—external limiting membrane; IPRL—interface between the inner and outer segments of the photoreceptor layer; RPE—retinal pigmented epithelium; C—choriocapillaris and choroid. A highly reflective spot in the center of the fovea is marked with an R. A blood vessel is marked with a large circle (BV) and structures in the outer plexiform layer are marked with smaller circles. FIG. 8 shows a graph of a coherence function obtained from a reflective spot in the fovea. For example, the coherence length is equal to 4.8 μm in air.

To summarize, in the graph shown in FIG. 5, the phase term θ(k) obtained from a mirror in a water-filled model eye (averaged over 100 A-lines) and from a spectral reflective spot in the human fovea (averaged over 5 A-lines, see FIG. 7) are illustrated. The differences between the measured phase terms and polynomial fits (9^(th) order) to the data are also shown, with the corresponding axis provided on a right side thereof. Both phases show approximately the same pattern, which indicates that the model eye and the real eye generally experience similar amounts of dispersion. The phase term obtained from the spectral reflection of the fovea can be used (e.g., curve 270 of FIG. 5) to remove chromatic dispersion artifacts in data obtained from a human subject in vivo, as shown in the graph of FIG. 7 and quantified in the graph of FIG. 8.

The coherence length can be determined in vivo from the spectral reflection in the center of the fovea labeled as R in FIG. 7, averaged over 5 A-lines. This coherence function is shown as a graph in FIG. 8, and the coherence length after dispersion compensation as shown in FIG. 8 as being equal to 4.8 μm in air and 3.5 μm in tissue (n=1.38). It is clear that without dispersion compensation, the coherence length is significantly longer (e.g., by a factor of 2-3), thus reducing the axial resolution considerably. In particular, the curve of FIG. 8 (similarly to the graph in FIG. 4) shows the results without the dispersion compensation is illustrated as a dashed line, and referred to by numeral 410, and the curve illustrating the results after the dispersion compensation has been successfully applied which is shown as a solid line, and referred to by numeral 420.

Practically, an exemplary embodiment of the system, process and software arrangement according to the present invention can also be described with reference to FIG. 9 which illustrates a flow diagram according to one exemplary embodiment of the present invention. As previously described, an area in the image containing a spectral reflection is selected (step 510). After such selection, the existing algorithm determines the amount of chromatic dispersion (step 520) and removes such dispersion from the image (step 530). As previously described, the dispersion can be removed by multiplying spectra in k-space with a phase e^(−iθ(k)). The earlier described polynomial fit can be used. Since the polynomial fit and the original phase are approximately similar (as shown in FIG. 5), it is also possible to use a measured phase curve. The selection procedure for selecting the location of the spectral reflection can be either a manual procedure or an automated procedure. Thereafter, a new image may be generated based on the originally-selected image, but with the dispersions that was removed according to the exemplary technique of the present invention (step 540).

The previously-described exemplary results may be obtained using a simple manual procedure, where the operator generally selects the specific portion of the image by hand, e.g., by determining the coordinates of the reflecting spots. Such procedure can be simplified with, e.g., MatLab software, in which the operator may be requested to draw a rectangular shape around a reflecting spot, (see numeral 600 in FIG. 10), thus selecting the location of the spectral spot. Using such exemplary selection of the portion of the image, the dispersion can be compensated using the compensation described above.

According to another exemplary embodiment of the present invention, spectral reflections can also be located automatically by using a particular technique. This exemplary technique can be based on an algorithm that finds a maximum signal For example, the signal returning from the spectral reflection, e.g., in the center of the fovea generally has a higher value than any of the other reflections. Using such exemplary technique, it is possible to select this reflecting spot automatically, and therefor manual input from an operator would not be necessary. with this technique, a feedback signal can be forwarded to the scanning apparatus, so that this apparatus monitors for the brightest spectral reflection in the sample 60 (e.g., the eye). For example, a series of smaller and smaller three-dimensional raster scans can be acquired, until the center of the fovea is located. If the subject moves during this operation, the raster scanning can expanded and confined the target image again. In another publication, an exemplary technique used to track the surface of the retina and compensate for motion artifacts has been described. See Cense, B. et al., “In Vivo Birefringence and Thickness Measurements of the Human Retinal Nerve Fiber Layer Using Polarization-Sensitive Optical Coherence Tomography”, Journal of Biomedical Optics, 2004, 9(1), pp. 121-125.

Another exemplary embodiment of the present invention uses compensated dispersion in dependence of depth. The technique according to the exemplary embodiment of the present invention described above is capable of compensating for a constant dispersion mismatch between the sample and the reference arm. However, with an increasing bandwidth available in the OCT imaging, dispersion broadening between superficial and deeper layers within an image may becomes important. The dispersion broadening may be due to the accumulated dispersion between the superficial and deeper layer.

Described herein below is a technique according to another exemplary embodiment of the present invention which is capable of depth dependent dispersion compensation, i.e., a correction for the dispersion that varies with depth. As is well known, the signal in SD-OCT and OFDI is defined by,

$\begin{matrix} {{I(k)} = {{I_{r}(k)} + {2\sqrt{{I_{s}(k)}{I_{r}(k)}}{\sum\limits_{n}{\alpha_{n}{\cos\left( {kz}_{n} \right)}}}} + {I_{s}(k)}}} & (2) \end{matrix}$ where I_(r)(k) and I_(s)(k) are the wavelength-dependent intensities reflected from the reference and sample arms, respectively, and k is the wave number. The second term on the right hand side of Eq. (2) represents the interference between the light signal returning from the reference and sample arms. α_(n) is the square root of the sample reflectivity at depth z_(n). As described in Hausler, G. et al., “Coherence Radar and Spectral Radar—New Tools for Dermatological Diagnosis”, J. Biomed. Opt., 1998, 3(1), pp. 21-31, depth information can be obtained by performing an inverse Fourier transform of Eq. (2), yielding the following convolution

$\begin{matrix} {{{{{FT}^{- 1}\left\lbrack {I(k)} \right\rbrack}}^{2} = {{\Gamma^{2}(z)} \otimes \begin{Bmatrix} {{\delta(0)} + {\sum\limits_{n}{\alpha_{n}^{2}{\delta\left( {z - z_{n}} \right)}}} +} \\ {{\sum\limits_{n}{\alpha_{n}^{2}{\delta\left( {z + z_{n}} \right)}}} + {O\left\lbrack {I_{s}^{2}/I_{r}^{2}} \right\rbrack}} \end{Bmatrix}}},} & (3) \end{matrix}$ with Γ(z) representing the envelope of the coherence function. The first term in the brackets on the right hand side refers to an autocorrelation signal from the reference arm, and has magnitude unity. The second and third terms are reflect the interference between light returning from the reference and sample arms and from two images, where each has magnitude on the order of I_(s)/I_(r). These two terms provide mirror images. The final term, with magnitude on the order of I_(s) ²/I_(r) ², describes autocorrelation noise due to interference within the sample arm. I_(s) and I_(r) represent the total intensity reflected from sample and reference arms, respectively.

Retaining only the interference term

${2\sqrt{{I_{s}(k)}{I_{r}(k)}}{\sum\limits_{n}{\alpha_{n}{\cos\left( {kz}_{n} \right)}}}},$ a constant dispersion mismatch can be described by introducing a phase term θ(k) in the cosine term,

$2\sqrt{{I_{s}(k)}{I_{r}(k)}}{\sum\limits_{n}{\alpha_{n}{{\cos\left( {{k\; z_{n}} + {\theta(k)}} \right)}.}}}$ The constant dispersion mismatch can be compensated for with the method described before. A depth dependent dispersion term is described by introducing a depth dependent phase term, f(k)z_(n) in the cosine term,

$2\sqrt{{I_{s}(k)}{I_{r}(k)}}{\sum\limits_{n}{\alpha_{n}{{\cos\left( {{kz}_{n} + {{f(k)}z_{n}}} \right)}.}}}$ The depth dependent dispersion term can be compensated for by a remapping operation of the data in k-space. The cosine term can be rewritten as

$2\sqrt{{I_{s}(k)}{I_{r}(k)}}{\sum\limits_{n}{\alpha_{n}{\cos\left( {k^{\prime}z_{n}} \right)}}}$ with k′=k+f(k). After the remapping operation, the data can be linearized in k-space before the Fourier transform resulting in Eq. (3).

The function f(k) can be determined by measuring the dispersion F(k)_(n) and F(k)_(m) at two different locations, z_(n) and z_(m) using the method described for a constant dispersion term, where the function f(k) is given by

${f(k)} = {\frac{{F(k)}_{m} - {F(k)}_{n}}{z_{m} - z_{n}}.}$ The locations for determining F(k)n and F(k)m are preferably locations in the material (tissue, vitrious, retina, coronary artery, etc) with strong reflections. Filtering the function f(k) to reject noise can be performed by retaining only a limited or predetermined number of coefficients from a polynomial or Fourier series fit to the data. This exemplary technique can be used to predetermine the dispersion in various materials or biological tissues, and utilize the determined values to implement depth dependent dispersion compensation during imaging or post processing of SD-OCT and OFDI data. For use in retinal data, several locations can provide strong reflections that can be used to determine the dispersion, such as the center of the fovea (fovealar umbo), external limiting membrane, interface between the inner and outer segments of the photoreceptor layer (“IPRL”) and retinal pigmented epitheleum (“RPE”). Spectral reflections can also be located on the inner limiting membrane, on top of the retinal nerve fiber layer. In order to see these reflections, the sample (e.g., the eye) should be tilted such that the surface thereof is exactly perpendicular to the beam.

A further technique according to yet another exemplary embodiment of the present invention can be used to determine a constant and depth dependent dispersion. For example, in the presence of constant and depth-dependent dispersion, the interference signal associated with the n-th reflection point in the sample can be defined by

$\begin{matrix} {{{I\left( {k,z_{s,n},z_{r}} \right)} = {2\sqrt{{I_{s}(k)}{I_{r}(k)}}\alpha_{n}{\cos\left\lbrack {{k\left( {z_{s,n} - z_{r}} \right)} + {{f(k)}z_{s,n}} + {\theta(k)}} \right\rbrack}}},} & (4) \end{matrix}$ where z_(s,n) refers to the distance of the reflection point from the surface of the sample, and z_(r) refers to the position of the reference mirror with respect to the sample surface. Shifting the position of the reference mirror to z_(r)′=2z_(s,n)−z_(r) provides the following

$\begin{matrix} \begin{matrix} {{I\left( {k,z_{s,n},z_{r}^{\prime}} \right)} = {2\sqrt{{I_{s}(k)}{I_{r}(k)}}\alpha_{n}{\cos\begin{bmatrix} {{- {k\left( {z_{s,n} - z_{r}} \right)}} + {{f(k)}z_{s,n}} +} \\ {{\theta(k)} + \delta} \end{bmatrix}}}} \\ {{= {2\sqrt{{I_{s}(k)}{I_{r}(k)}}\alpha_{n}{\cos\begin{bmatrix} {{k\left( {z_{s,n} - z_{r}} \right)} - {{f(k)}z_{s,n}} -} \\ {{\theta(k)} - \delta} \end{bmatrix}}}},} \end{matrix} & (5) \end{matrix}$ where δ refers to any possible phase error introduced in the measurement. It is possible to determine the phase functions, φ(k,z_(s,n),z_(r)) and φ(k,z_(s,n),z_(r)′) of the interference signals in Eq. (4) and (5), respectively. It follows that φ(k,z _(s,n) ,z _(r))−φ(k,z _(s,n) ,z _(r)′)=2f(k)z _(s,n)+2θ(k)+δ  (6)

The third-term on right hand side, a constant phase error, can be differentiated from the 1^(st) and 2^(nd) terms which are both dependent on k. By measuring the differential phase for multiple reflection points in the sample or for multiple z_(s,n) where n=1 to N, it is possible to determine f(k) and θ(k).

If the constant dispersion is negligible or has been canceled, it is possible to locate the best or preferable mapping function that leads to transform-limited point spread function for each position of the reference mirror. The preferable mapping function may be defined by k′=k+j(k) for the signal represented in Eq. (4) and k′=k−f(k) for Eq. (5). Therefore, subtracting the two mapping functions can yield the depth-dependent dispersion f(k). Instead of shifting the reference mirror, the mirror can be placed so that the zero delay corresponds to (either approximately or exactly) the middle of the two reflection points in the sample. The interference signal associated with the two reflections can be simultaneously measured and analyzed to determine the dispersion.

FIG. 11 shows another exemplary embodiment of the process according to the present invention which can be used to control the dispersion of the data associated with the image obtained from the reference and sample arms. For example, a detector (e.g., the detectors of the arrangements shown in FIG. 1 and/or 2) received and detect an interference signal which contains data associated with the electromagnetic radiation received from the sample arm and the reference arm (step 605), and then generates a spectrum signal I(k) based on the detected interference signal (step 610). This spectrum signal I(k) is forwarded to the processing arrangement, e.g., as data, which performs a Fast Fourrier Transform (“FFT”) on the spectrum signal I(k) (step 615). Thereafter, an initial signal I(z) associated with the spectrum signal I(k) is set to 0 for z>0 and z<0 (step 620), and in step 625, an absolute values for the initial signal I(z) is set. In step 630, a signal I(k) is generated based on the detected signal, a window of interest of the image may be determined in step 635. Such are of interest can be a region of the peak of the absolute value signal (ABS(I(z))), a center peak at around z−0 by shifting the signal, etc. The window can be obtained automatically by the processing arrangement and/or manually by an operator.

In step 640, an inverse FFT is performed on the signal I(z), and a phase term θ(k) of the transformed I(z) signal is determined (step 645). In step 650, the exemplary process according to the present invention the phase function that can apply a polynomial of the order of N to θ(k), e.g., by subtracting the polynomial fit of 9^(th) order, yielding a set of coefficients α₁₋₉. As described herein, the phase θ(k) may be obtained from a mirror in a model eye and from a spectral reflection in the fovea. The filtered phase term can then be determined from the polynomial fit parameters/coefficients, e.g., by setting the first two polynomial coefficients to zero. In step 260, the filtered phase of the signal e^(−iθ(k)) can be stored for use in multiple images. Then, in step 665, a correction curve of the filtered phase term θ(k) can be applied, e.g., by multiplying all spectra of the image may be multiplied by e^(−iθ(k)). Finally, in step 670, dispersion corrected spectrum S′(k)=S(k) e^(−iθ(k)) may be used to calculate image intensity, birefringence and/or flow information.

The foregoing merely illustrates the principles of the invention. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. For example, the invention described herein is usable with the exemplary methods, systems and apparatus described in U.S. Patent Application No. 60/514,769. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements and methods which, although not explicitly shown or described herein, embody the principles of the invention and are thus within the spirit and scope of the present invention. In addition, all publications, patents and patent applications referenced above are incorporated herein by reference in their entireties. 

1. A system to compensate for a dispersion in at least one portion of an image, comprising: a processing arrangement configured to obtain information associated with the at least one portion of the image, the at least one portion of the image being associated with the interference signal that includes a first electro-magnetic radiation received from a sample and a second electro-magnetic radiation received from a reference, wherein the processing arrangement is configured to determine (i) complex spectral data that is based the interference signal, and (ii) a phase of at least one spectral component of the complex spectral data, and wherein the processing arrangement is further configured to compensate for the dispersion in the at least one portion by controlling the phase of the at least one spectral component of the complex spectral data.
 2. The system according to claim 1, wherein the dispersion is an indication of a difference between the first and second electro-magnetic radiations.
 3. The system according to claim 1, wherein the processing arrangement is configured to control the dispersion by at least one of reducing and removing the dispersion in the at least one portion of the image.
 4. The system according to claim 1, wherein the processing arrangement is further configured to determine data associated with reflective layers in a tissue of the sample from the interference signal, and determining information associated with the dispersion that is provided in the data.
 5. The system according to claim 4, wherein the processing arrangement is further configured to utilize the information to at least one of reduce and remove the dispersion from the data.
 6. The system according to claim 1, wherein, when the processing arrangement executes software instructions, the processing arrangement is configured to control the phase of the at least one spectral component of the interference signal.
 7. The system according to claim 1, wherein, prior to controlling the phase of the at least one spectral component of the interference signal, the processing arrangement is configured to quantify the dispersion, and correct for the dispersion in the image based on the quantification.
 8. The system according to claim 1, wherein the dispersion is a chromatic dispersion.
 9. The system according to claim 1, wherein the processing arrangement is further configured to determine data associated with the dispersion of the image, quantify the dispersion using the data, and correct for the dispersion in the image based on the quantification.
 10. The system according to claim 9, wherein the sample is a retina of an eye.
 11. The system according to claim 10, wherein the information includes data associated with spectral reflections obtained from the retina.
 12. The system according to claim 11, wherein the processing arrangement is configured to enable an operator to select at least one dispersed spectral reflection of the spectral reflections.
 13. The system according to claim 12, wherein the at least one dispersed spectral reflection is selected using a graphical user interface.
 14. The system according to claim 12, wherein the at least one dispersed spectral reflection is selected at least one of during an acquisition of the image and after the acquisition of the image.
 15. The system according to claim 12, wherein the processing arrangement is further configured to quantify the dispersion using the at least one dispersed spectral reflection, and correct for the dispersion in the image based on the quantification.
 16. The system according to claim 12, wherein the processing arrangement is further configured to interactively search for a brightest one of the spectral reflections, quantify the dispersion using the brightest one of the spectral reflections, and correct for the dispersion in the image based on the quantification.
 17. The system according to claim 1, wherein the dispersion is a depth dependent chromatic dispersion.
 18. The system according to claim 17, wherein the information includes dispersed image data, and wherein the processing arrangement is further configured to quantify the dispersion using the dispersed image data, and correct for the dispersion in the image based on the quantification.
 19. The system according to claim 18, wherein the sample is a retina of an eye.
 20. The system according to claim 17, wherein the dispersed image data includes spectral reflections, and wherein the processing arrangement is configured to quantify the dispersion using the spectral reflections.
 21. The system according to claim 1, wherein the processing arrangement is configured to control the dispersion by correcting the dispersion in the image using predetermined constant chromatic dispersion parameters.
 22. The system according to claim 21, wherein the dispersion is compensated based on an estimate of an axial eye length.
 23. The system according to claim 21, wherein the dispersion is compensated based on an estimate of an axial eye length.
 24. A method to compensate for a dispersion in at least one portion of an image, comprising: obtaining information associated with the at least one portion of the image, the at least one portion of the image being associated with an interference signal that includes a first electro-magnetic radiation received from a sample and a second electro-magnetic radiation received from a reference; determining (i) complex spectral data that is based the interference signal, and (ii) a phase of at least one spectral component of the complex spectral data; and compensating for the dispersion in the at least one portion of the image by controlling the phase of the at least one spectral component of the complex spectral data.
 25. The method according to claim 24, wherein the dispersion is an indication of a difference between the first and second electro-magnetic radiations.
 26. The method according to claim 24, wherein the controlling step includes the substep of at least one of reducing and removing the dispersion in the at least one portion of the image.
 27. The method according to claim 24, further comprising the steps of: determining data associated with reflective layers in a tissue of the sample from the interference signal; and determining information associated with the dispersion that is provided in the data.
 28. The method according to claim 27, further comprising the step of utilizing the information to at least one of reduce and remove the dispersion from the data.
 29. The method according to claim 24, wherein the controlling step is performed using software instructions.
 30. The method according to claim 24, further comprising the steps of, prior to the controlling step, quantifying the dispersion; and correcting for the dispersion in the image based on the quantification.
 31. The method according to claim 24, wherein the dispersion is a chromatic dispersion.
 32. The method according to claim 24, further comprising the steps of: determining data associated with the dispersion of the image; quantifying the dispersion using the data; and correcting for the dispersion in the image based on the quantification.
 33. The method according to claim 32, wherein the sample is a retina of an eye.
 34. The method according to claim 33, wherein the information includes data associated with spectral reflections obtained from the retina.
 35. The method according to claim 33, further comprising the step of enabling an operator to select at least one dispersed spectral reflection of the spectral reflections.
 36. The method according to claim 35, wherein the at least one dispersed spectral reflection is selected using a graphical user interface.
 37. The method according to claim 35, wherein the at least one dispersed spectral reflection is selected at least one of during an acquisition of the image and after the acquisition of the image.
 38. The method according to claim 35, further comprising the steps of: quantifying the dispersion using the at least one dispersed spectral reflection; and correcting for the dispersion in the image based on the quantification.
 39. The method according to claim 35, further comprising the steps of: interactively searching for a brightest one of the spectral reflections; quantifying the dispersion using the brightest one of the spectral reflections; and correcting for the dispersion in the image based on the quantification.
 40. The method according to claim 24, wherein the dispersion is a depth dependent chromatic dispersion.
 41. The method according to claim 40, wherein the information includes dispersed image data, and further comprising the steps of: quantifying the dispersion using the dispersed image data; and correcting for the dispersion in the image based on the quantification.
 42. The method according to claim 41, wherein the sample is a retina of an eye.
 43. The method according to claim 40, wherein the dispersed image data includes spectral reflections, and wherein the processing arrangement is adapted to quantify the dispersion using the spectral reflections.
 44. The method according to claim 43, further comprising the step of controlling the dispersion by correcting the dispersion in the image using predetermined constant chromatic dispersion parameters.
 45. The method according to claim 44, wherein the dispersion is corrected based on an estimate of an axial eye length.
 46. The method according to claim 44, wherein the dispersion is compensated based on an estimate of an axial eye length.
 47. A computer program adapted to compensate for a dispersion in at least one portion of an image for execution by a processing arrangement, said computer program comprising instructions for performing a method comprising: obtaining information associated with the at least one portion of the image, the at least one portion of the image being associated with an interference signal that includes a first electro-magnetic radiation received from a sample and a second electro-magnetic radiation received from a reference; determining (i) complex spectral data that is based the interference signal, and (ii) a phase of at least one spectral component of the complex spectral data; and compensating for the dispersion in the at least one portion of the image by controlling the phase of the at least one spectral component of the complex spectral data. 